From 5d507536e19590dd68c5dc057ad0238794a8b44c Mon Sep 17 00:00:00 2001 From: Lars Bogner Date: Sun, 24 Mar 2024 17:37:09 +0100 Subject: [PATCH] Quartz sync: Mar 24, 2024, 5:37 PM --- content/Altprotokolle/Frage Beta-Zerfall.md | 2 +- .../Grundlagen/Synchrotronstrahlung.md | 8 ++++++++ .../Grundlagen/Übergangsstrahlung.md | 3 +++ .../Streuexperimente zur Strukturanalyse.md | 4 ++-- content/Einheiten und Größenordnungen.md | 5 +++++ .../Brookhaven National Labratory.md | 2 +- content/Experimente/Projekt Poltergeist.md | 2 +- content/Experimente/SLAC.md | 2 +- content/Liste der Altprotokolle.md | 10 +++++----- .../Atomphysik/Absorption und Emission.md | 2 +- .../Stochastische Verteilungen.md | 2 ++ .../Standard-Modell/Feynman-Diagramme.md | 3 +++ .../Standard-Modell/Isospin.md | 1 + .../Standard-Modell/Resonanzen.md | 2 +- content/Wasserstoffatom/Atommodelle.md | 4 +++- .../Kernspin und Hyperfeinstruktur.md | 2 +- .../fig/Feynman-Diagramme-Zusammenfassung.pdf | Bin 0 -> 1093998 bytes content/fig/rutherford_mott.png | Bin 0 -> 39371 bytes content/fig/teilchenlebensdauern.png | Bin 0 -> 820143 bytes content/fig/teilchenmassen.png | Bin 0 -> 736684 bytes quartz.config.ts | 6 +++--- 21 files changed, 42 insertions(+), 18 deletions(-) create mode 100644 content/Detektor und Beschleunigertechnologie/Grundlagen/Synchrotronstrahlung.md create mode 100644 content/Physikalische Grundlagen/Standard-Modell/Feynman-Diagramme.md create mode 100644 content/fig/Feynman-Diagramme-Zusammenfassung.pdf create mode 100644 content/fig/rutherford_mott.png create mode 100644 content/fig/teilchenlebensdauern.png create mode 100644 content/fig/teilchenmassen.png diff --git a/content/Altprotokolle/Frage Beta-Zerfall.md b/content/Altprotokolle/Frage Beta-Zerfall.md index dd698b1..ff1282d 100644 --- a/content/Altprotokolle/Frage Beta-Zerfall.md +++ b/content/Altprotokolle/Frage Beta-Zerfall.md @@ -7,7 +7,7 @@ # Antwort -Ein [[Neutron]] wird zu [[Proton]] und [[Elektron]] + [[Neutrino]] umgewandelt. Für eine genauere Erläuterung siehe [[Kernprozesse#Der Beta-Zerfall]]. +Ein [[Neutron]] wird zu [[Proton]] und [[Elektron]] + [[Neutrino]] umgewandelt. Für eine genauere Erläuterung siehe [[Kernprozesse#Der Beta-Zerfall]] und das nachfolgende [[Feynman-Diagramme]] ![[Feynman_Beta_Negative_Decay.svg]] Im $\beta^{+}$-Zerfall kommt es zur Umwandlung von einem [[Proton]] zu einem [[Neutron]] mit Positron und Neutrino. Der Zerfall ist energetisch nur möglich wenn die Bindungsenergie im Kern sich danach stark verbessert, da sonst energetisch gehindert. (Kerne mit sehr vielen Protonen -> [[Bethe-Weizsäcker-Formel]]). diff --git a/content/Detektor und Beschleunigertechnologie/Grundlagen/Synchrotronstrahlung.md b/content/Detektor und Beschleunigertechnologie/Grundlagen/Synchrotronstrahlung.md new file mode 100644 index 0000000..72003eb --- /dev/null +++ b/content/Detektor und Beschleunigertechnologie/Grundlagen/Synchrotronstrahlung.md @@ -0,0 +1,8 @@ +--- +aliases: + - Synchrotronlicht +--- + +#class/Ex-IV #beschleuniger +Die **[[Synchrotron]]strahlung** bezeichnet die elektromagnetische Abstrahlung beschleunigter Ladungen, welche auf eine **Kreisbahn** gezwungen werden. +Die Abstrahlung erfolgt tangential. \ No newline at end of file diff --git a/content/Detektor und Beschleunigertechnologie/Grundlagen/Übergangsstrahlung.md b/content/Detektor und Beschleunigertechnologie/Grundlagen/Übergangsstrahlung.md index c206781..560f207 100644 --- a/content/Detektor und Beschleunigertechnologie/Grundlagen/Übergangsstrahlung.md +++ b/content/Detektor und Beschleunigertechnologie/Grundlagen/Übergangsstrahlung.md @@ -2,6 +2,9 @@ Wenn ein ultra-relativistisches Teilchen eine Grenzfläche zwischen zwei Medien mit unterschiedlicher Permittivität passiert, wird die sogenannte Übergangsstrahlung emittiert. Es werden keV-Photonen in Vorwärts-Richtung emittiert. +Eine mögliche Erklärung sind die Spiegelladungen in Materialien mit Permittivität, wobei der Unterschied der Permittivität dazu führt, dass ein zeitlich verändernder Dipol entsteht, welcher [[Photon]]en aussendet. +Übergangsstrahlung entsteht auch zu geringen Teilen in einer [[Röntgenstrahlung|Röntgenröhre]]. + *Folder tags:* diff --git a/content/Detektor und Beschleunigertechnologie/Streuexperimente zur Strukturanalyse.md b/content/Detektor und Beschleunigertechnologie/Streuexperimente zur Strukturanalyse.md index ef38e6d..05b709e 100644 --- a/content/Detektor und Beschleunigertechnologie/Streuexperimente zur Strukturanalyse.md +++ b/content/Detektor und Beschleunigertechnologie/Streuexperimente zur Strukturanalyse.md @@ -27,7 +27,7 @@ $$ \left(\frac{d \sigma}{d \Omega}\right)_\text{Mott} = \left(\frac{d \sigma}{d \Omega}\right)_\text{Rutherford} \cdot \frac{E_f}{E_{i}}(1 - \beta^{2}\sin^2(\frac{\theta}{2})) $$ - +![[rutherford_mott.png]] ## Formfaktor Die Streuung an ausgedehnten Objekten bedarf der Einführung des Formfaktors. Bei hohem Impulstransfer $|\vec{q}|$ . Falls die *de-Broglie-Wellenlänge* des Projektils $\lambda \approx R$ (Kernradius) finden wir Abweichungen, welche durch den Formfaktor $F(\vec{q})$ ausgeglichen werden. @@ -47,7 +47,7 @@ Bei solch einem hohen Impulstransfer koppeln die Elektronen an die Ladung und da $$ \left(\frac{d \sigma}{d \Omega}\right)_\text{exp} = \left(\frac{d \sigma}{d \Omega}\right)_\text{Mott} \cdot \left(\underbrace{\frac{G_{E}^{2}+ \frac{Q^2}{4M^{2}}G_{M}^2}{1+\frac{Q^2}{4M^{2}}}}_{\theta \text{ unabh.}} +\underbrace{\frac{Q^2}{2M^{2}}G_M^2\tan^2(\theta/2)}_{\theta\text{ abh.}}\right) $$ -mit dem magnetischen und elektrischen Formfaktor $G_{M/E}(Q^2)$. Dieser Wirkungsquerschnitt wird auch gerne zur Rosenbluth-Formel verallgemeinert mit +mit dem magnetischen und elektrischen Formfaktor $G_{M/E}(Q^2)$. Dieser Wirkungsquerschnitt wird auch gerne zur *Rosenbluth-Formel* verallgemeinert mit $$ A(Q^{2)} + B(Q^{2)}\tan^2(\frac{\theta}{2}) $$ diff --git a/content/Einheiten und Größenordnungen.md b/content/Einheiten und Größenordnungen.md index 90a3a4a..911a238 100644 --- a/content/Einheiten und Größenordnungen.md +++ b/content/Einheiten und Größenordnungen.md @@ -32,6 +32,11 @@ Nach der Entdeckung des [[J psi]] kam es zu immer weiteren suchen nach doppelten Seit dem wird in der Teilchenphysik bei neuen Entdeckungen stets eine Signifikanz von $> 5 \sigma$ gefordert. +![[teilchenmassen.png]] +![[teilchenlebensdauern.png]] + + + *Folder tags:* *No folder tags* \ No newline at end of file diff --git a/content/Experimente/Brookhaven National Labratory.md b/content/Experimente/Brookhaven National Labratory.md index d61879b..eb53e68 100644 --- a/content/Experimente/Brookhaven National Labratory.md +++ b/content/Experimente/Brookhaven National Labratory.md @@ -17,7 +17,7 @@ Einige der herausragenden Errungenschaften von Brookhaven umfassen: Brookhaven verfügt über mehrere hochrangige Forschungseinrichtungen: - **RHIC (Relativistic Heavy Ion Collider)**: Ein Beschleuniger, der hochenergetische Kollisionen zwischen schweren Ionen ermöglicht, um Zustände der Materie unter extremen Bedingungen zu untersuchen. -- **NSLS-II (National Synchrotron Light Source II)**: Eine der weltweit hellsten Synchrotronlichtquellen, die Forschern aus einer Vielzahl von Disziplinen fortschrittliche Imaging- und Analysetechniken bietet. +- **NSLS-II (National Synchrotron Light Source II)**: Eine der weltweit hellsten [[Synchrotronstrahlung|Synchrotronlicht]]quellen, die Forschern aus einer Vielzahl von Disziplinen fortschrittliche Imaging- und Analysetechniken bietet. - **Center for Functional Nanomaterials**: Ein Forschungszentrum, das auf die Entwicklung von Nanotechnologien ausgerichtet ist. ### Aktuelle Nutzung und Bedeutung diff --git a/content/Experimente/Projekt Poltergeist.md b/content/Experimente/Projekt Poltergeist.md index b127dfe..7f783d5 100644 --- a/content/Experimente/Projekt Poltergeist.md +++ b/content/Experimente/Projekt Poltergeist.md @@ -1,6 +1,6 @@ #class/Ex-V-II #experiment #neutrino -Das Experiment von *Cowan* und *Reines* mit dem Detektor *Herr Auge* zum Nachweis der Neutrinos konnte erstmals die Existenz der [[Neutrino]]s nachweisen. Die Messung beruht auf der inversen $\beta$-Interaktion ([[Kernprozesse#Der Beta-Zerfall]]) eines Neutrinos mit einem Proton nach dem folgenden Feynman-Diagramm +Das Experiment von *Cowan* und *Reines* mit dem Detektor *Herr Auge* zum Nachweis der Neutrinos konnte erstmals die Existenz der [[Neutrino]]s nachweisen. Die Messung beruht auf der inversen $\beta$-Interaktion ([[Kernprozesse#Der Beta-Zerfall]]) eines Neutrinos mit einem Proton nach dem folgenden [[Feynman-Diagramme]] ![[inverse-beta-decay.png]] Den hohen notwendigen Neutrinofluss, welcher benötigt wurde, stammte aus einem Kernreaktor im Rahmen des Savannah River Areals. Der Fluss ist notwendig aufgrund eines sehr geringen Wirkungsquerschnitts. Der Detektor besteht aus zwei Wassertanks getrennt durch ein *liquid scintillator* und Detektion über [[Photomultiplier]] mit einer Koinzidenzschaltung, da das Positron annihiliert und zwei Gammas entsendet werden. diff --git a/content/Experimente/SLAC.md b/content/Experimente/SLAC.md index 9ffc7c4..3acfe6b 100644 --- a/content/Experimente/SLAC.md +++ b/content/Experimente/SLAC.md @@ -18,7 +18,7 @@ Das Hauptziel des SLAC ist die Erforschung der fundamentalen Struktur des Univer - **Teilchenphysik**: Untersuchung der fundamentalen Teilchen und Kräfte, einschließlich der Suche nach neuer Physik jenseits des Standardmodells. - **Astroteilchenphysik und Kosmologie**: Erforschung des Universums auf den größten Skalen, einschließlich der dunklen Materie und der dunklen Energie. -- **Materialwissenschaften und Chemie**: Nutzung von Synchrotronlichtquellen und Freie-Elektronen-Lasern zur Untersuchung der Eigenschaften von Materialien und chemischen Reaktionen auf atomarer Ebene. +- **Materialwissenschaften und Chemie**: Nutzung von [[Synchrotronstrahlung|Synchrotronlicht]]quellen und Freie-Elektronen-Lasern zur Untersuchung der Eigenschaften von Materialien und chemischen Reaktionen auf atomarer Ebene. - **Biophysik und Medizinische Physik**: Anwendung von Röntgenstrahltechniken zur Untersuchung biologischer Moleküle und Prozesse, mit dem Ziel, neue Einblicke in lebenswichtige biologische Systeme und Krankheitsmechanismen zu gewinnen. Das SLAC National Accelerator Laboratory bleibt an der vordersten Front der Forschung, indem es ständig neue Technologien entwickelt und anwendet, um die Geheimnisse des Universums zu entschlüsseln. diff --git a/content/Liste der Altprotokolle.md b/content/Liste der Altprotokolle.md index 5339048..bdc6d38 100644 --- a/content/Liste der Altprotokolle.md +++ b/content/Liste der Altprotokolle.md @@ -1,15 +1,15 @@ #altprotokoll -- [ ] Altprotokoll vom 2023-12-21: [[Notizen_2023-12-21_Altprotokoll_Wolf|Link zum Protokoll]] +- [x] Altprotokoll vom 2023-12-21: [[Notizen_2023-12-21_Altprotokoll_Wolf|Link zum Protokoll]] - [ ] Altprotokoll vom 2023-12-18: [[Notizen_2023-12-18_Altprotokoll_Wolf|Link zum Protokoll]] -- [ ] Altprotokoll vom 2023-11-10: [[Notizen_2023-11-10_Altprotokoll_Wolf|Link zum Protokoll]] +- [x] Altprotokoll vom 2023-11-10: [[Notizen_2023-11-10_Altprotokoll_Wolf|Link zum Protokoll]] - [ ] Altprotokoll vom 2023-10-30: [[Notizen_2023-10-30_Altprotokoll_Wolf|Link zum Protokoll]] - [ ] Altprotokoll vom 2023-09-28: [[Notizen_2023-09-28_Altprotokoll_Wolf|Link zum Protokoll]] -- [ ] Altprotokoll vom 2023-09-19: [[Notizen_2023-09-19_Altprotokoll_Wolf|Link zum Protokoll]] -- [ ] Altprotokoll vom 2023-09-14: [[Notizen_2023-09-14_Altprotokoll_Wolf|Link zum Protokoll]] +- [x] Altprotokoll vom 2023-09-19: [[Notizen_2023-09-19_Altprotokoll_Wolf|Link zum Protokoll]] *quasi fertig* +- [x] Altprotokoll vom 2023-09-14: [[Notizen_2023-09-14_Altprotokoll_Wolf|Link zum Protokoll]] *quasi fertig* - [ ] Altprotokoll vom 2023-06-06: [[Notizen_2023-06-06_Altprotokoll_Wolf|Link zum Protokoll]] - [ ] Altprotokoll vom 2023-02-09: [[Notizen_2023-02-09_Altprotokoll_Wolf|Link zum Protokoll]] - [ ] Altprotokoll vom 2022-11-07: [[Notizen_2022-11-07_Altprotokoll_Wolf|Link zum Protokoll]] -- [ ] Altprotokoll vom 2022-10-19: [[Notizen_2022-10-19_Altprotokoll_Wolf|Link zum Protokoll]] +- [x] Altprotokoll vom 2022-10-19: [[Notizen_2022-10-19_Altprotokoll_Wolf|Link zum Protokoll]] - [x] Altprotokoll vom 2022-09-08: [[Notizen_2022-09-08_Altprotokoll_Wolf|Link zum Protokoll]] - [ ] Altprotokoll vom 2022-09-00: [[Notizen_2022-09-00_Altprotokoll_Wolf|Link zum Protokoll]] - [ ] Altprotokoll vom 2019-12-19: [[Notizen_2019-12-19_Altprotokoll_Wolf|Link zum Protokoll]] diff --git a/content/Physikalische Grundlagen/Atomphysik/Absorption und Emission.md b/content/Physikalische Grundlagen/Atomphysik/Absorption und Emission.md index a15b04e..71354ea 100644 --- a/content/Physikalische Grundlagen/Atomphysik/Absorption und Emission.md +++ b/content/Physikalische Grundlagen/Atomphysik/Absorption und Emission.md @@ -13,7 +13,7 @@ Die Rate für die Absorption und die stimulierte Emission ist gegeben durch [[Fe Diese Regel folgt direkt aus der [[Störungstheorie]]. Die Funktion $\rho(\omega)$ beschreibt dabei die Zustandsdichte der einfallenden [[Photon]]en. Um diese Dichte zu bestimmen betrachten wir die theoretische Anzahl an Photonen in Abhängigkeit der Kreisfrequenz $$N(\omega) = 2 \cdot \frac{4}{3} \pi r^3 = \frac{8 \pi L^3 \omega^3}{3 (2\pi)^3 c^3} = \frac{V}{2 \pi^2 c^3} \omega^3$$ Zur Herleitung dieser wurde mehrfach die Näherung des [[Atommodelle#Bohrsche Atommodell]] genutzt. Somit folgt die Photonendichtefunktion als $$\Rightarrow \rho(\omega) = \frac{\partial N}{\partial \omega} = \frac{3}{2} \frac{V}{\pi^2 c^3} \omega^2$$ -Nun verbleibt es die Rate der spontanen Emission $S$ zu berechnen. *Einstein* postulierte hierfür, dass man die spontane Emission als stimulierte Emission durch [[Wärmestrahlung|Schwarzkörperstrahlung]] verstehen könne. Für die **Hohlraumstrahlung** gilt im thermischen Gleichgewicht $$N = N_0 e^{- \frac{\hbar \omega}{k_B T}}$$ und die Energiedichte dieser ist gegeben durch die *Lorentzkurve* $$I(\omega) = \frac{\hbar \omega^2}{\pi^2 c^3} \frac{1}{e^{\frac{\hbar \omega}{k_B T}} - 1}$$ +Nun verbleibt es die Rate der spontanen Emission $S$ zu berechnen. *Einstein* postulierte hierfür, dass man die spontane Emission als stimulierte Emission durch [[Wärmestrahlung|Schwarzkörperstrahlung]] verstehen könne. Für die **Hohlraumstrahlung** gilt im thermischen Gleichgewicht $$N = N_0 e^{- \frac{\hbar \omega}{k_B T}}$$ und die Energiedichte dieser ist gegeben durch die *Lorentzkurve* (siehe [[Resonanzen]]) $$I(\omega) = \frac{\hbar \omega^2}{\pi^2 c^3} \frac{1}{e^{\frac{\hbar \omega}{k_B T}} - 1}$$ ![[Ex4_0723_Lorentzkurve.png]] Ohne Beweis werde an dieser Stelle angegeben, dass somit die Rate der spontanen Emission folgt als $$ diff --git a/content/Physikalische Grundlagen/Quantenmechanik/Stochastische Verteilungen.md b/content/Physikalische Grundlagen/Quantenmechanik/Stochastische Verteilungen.md index 6a52bd3..d2811a5 100644 --- a/content/Physikalische Grundlagen/Quantenmechanik/Stochastische Verteilungen.md +++ b/content/Physikalische Grundlagen/Quantenmechanik/Stochastische Verteilungen.md @@ -23,6 +23,8 @@ Insbesondere kommt es dabei auf die Unterschiede in der [[Mathematik der Bosonen ![[Verteilungen.png]] +# *Breit-Wigner*-Verteilung +![[Resonanzen]] *Folder tags:* diff --git a/content/Physikalische Grundlagen/Standard-Modell/Feynman-Diagramme.md b/content/Physikalische Grundlagen/Standard-Modell/Feynman-Diagramme.md new file mode 100644 index 0000000..883f724 --- /dev/null +++ b/content/Physikalische Grundlagen/Standard-Modell/Feynman-Diagramme.md @@ -0,0 +1,3 @@ +#class/Ex-V-II #begriffsdefinition #SM + +![[Feynman-Diagramme-Zusammenfassung.pdf]] \ No newline at end of file diff --git a/content/Physikalische Grundlagen/Standard-Modell/Isospin.md b/content/Physikalische Grundlagen/Standard-Modell/Isospin.md index 0ff7aeb..bfe6a37 100644 --- a/content/Physikalische Grundlagen/Standard-Modell/Isospin.md +++ b/content/Physikalische Grundlagen/Standard-Modell/Isospin.md @@ -11,6 +11,7 @@ Der Schwache Isospin $I$ bzw. $T$ bildet die Symmetriegruppe $SU(2)$ . - Alle *chiral rechtshändigen* Teilchen bilden Singuletts bzgl. der Gruppe - -> keine CC-Wechselwirkung mit $W$-Bosonen aber NC-Prozesse möglich (siehe [[Ströme der Teilchenphysik]], [[Elektroschwache Vereinigung]]) +Die [[Schwache Wechselwirkung]] interagiert mit allen Teilchen mit **Isospin** $T \neq 0$. *Folder tags:* diff --git a/content/Physikalische Grundlagen/Standard-Modell/Resonanzen.md b/content/Physikalische Grundlagen/Standard-Modell/Resonanzen.md index 6c2f61e..e4547fd 100644 --- a/content/Physikalische Grundlagen/Standard-Modell/Resonanzen.md +++ b/content/Physikalische Grundlagen/Standard-Modell/Resonanzen.md @@ -10,7 +10,7 @@ $$ \Gamma \approx \frac{\hbar}{\tau} $$ mit der Lebensdauer eines Zustands $\tau$. - +Die **Breit-Wigner-Verteilung** wird auch als **Lorentzkurve** bezeichnet. *Folder tags:* diff --git a/content/Wasserstoffatom/Atommodelle.md b/content/Wasserstoffatom/Atommodelle.md index 821f6c0..85ca4e2 100644 --- a/content/Wasserstoffatom/Atommodelle.md +++ b/content/Wasserstoffatom/Atommodelle.md @@ -57,7 +57,9 @@ $$ \frac{d \sigma}{d \Omega} = (2 m_{e}Z \alpha)^{2}\frac{1}{q^{4}}\qquad \text{mit} \qquad q = 2 p \sin(\frac{\theta}{2}) $$ Da die Streuung aufgrund der geringen Energie der $\alpha$-Teilchen im Ruhterford-Prozess jedoch nur am $\frac{1}{r}$-Potential des Kerns geschieht, ist keine genaue Auflösung der Kernstruktur oder **-größe** möglich. +Bei höheren Energien kommen Effekte wie durch die [[Streuexperimente zur Strukturanalyse#Mott-Streeung]] und den [[Streuexperimente zur Strukturanalyse#Formfaktor]] hinzu. +![[rutherford_mott.png]] Dies führte zu einem Vergleich mit dem Sonnensystem, bei dem die Elektronen um den Kern kreisen wie Planeten um die Sonne. Allerdings ergibt sich ein fundamentales Problem mit dieser Analogie: Nach den Gesetzen der klassischen Physik müssten sich bewegende Elektronen kontinuierlich Energie in Form von elektromagnetischer Strahlung abgeben und schließlich in den Kern stürzen, was in der Realität nicht beobachtet wird. Dieser Widerspruch zur klassischen Physik deutet auf die Notwendigkeit einer neuen Theorie hin, die später als Quantenmechanik bekannt wurde. @@ -70,7 +72,7 @@ Die Vorstellung, dass Elektronen in diskreten Bahnen um den Atomkern kreisen und $$R_H = \frac{m_r c^2}{2} \alpha^2 Z^2$$ Bohr stellt dabei **3 Postulate** auf: -1. Dem Elektron stehen nicht alle klassisch möglichen Bahnen zur Verfügung, sondern nur bestimmte ausgewählte von ihnen. Auf diesen Bahnen erzeugt es keine elektromagnetische Strahlung, sondern behält seine Energie. Dies sind die stationären Zustände des Atoms. +1. Dem Elektron stehen nicht alle klassisch möglichen Bahnen zur Verfügung, sondern nur bestimmte ausgewählte von ihnen. Auf diesen Bahnen erzeugt es keine elektromagnetische Strahlung ([[Synchrotronstrahlung]]), sondern behält seine Energie. Dies sind die stationären Zustände des Atoms. 2. Das Elektron kann von einem stationären Zustand in einen anderen springen. Dieser als Quantensprung bezeichnete Vorgang liegt außerhalb des Gültigkeitsbereichs der klassischen Mechanik und der Elektrodynamik. Beim Quantensprung zwischen stationären Zuständen mit verschiedener Energie, den Energieniveaus, wird elektromagnetische Strahlung emittiert oder absorbiert. Dabei wird die Frequenz $f$ der Strahlung nicht durch die Umlauffrequenz des Elektrons bestimmt, sondern ausschließlich durch die Energiedifferenz $\Delta E$ der beiden Zustände nach der von Max Planck für die Wärmestrahlung entdeckten Formel $f = \frac{\Delta E}{h}$ 3. Die Frequenz der erzeugten oder absorbierten Strahlung nähert sich der Umlauffrequenz des Elektrons an, wenn sich das Elektron im Anfangszustand nur langsam bewegt und in den energetisch nächstgelegenen Zustand springt. ## Erweiterung durch Sommerfeld diff --git a/content/Wasserstoffatom/Kernspin und Hyperfeinstruktur.md b/content/Wasserstoffatom/Kernspin und Hyperfeinstruktur.md index 02c9a1d..c35fd7a 100644 --- a/content/Wasserstoffatom/Kernspin und Hyperfeinstruktur.md +++ b/content/Wasserstoffatom/Kernspin und Hyperfeinstruktur.md @@ -11,7 +11,7 @@ Die Stärke des Magnetfeldes am Kernort ($r=0$) wird durch $\left|\vec{B}_0\righ ## Lamb-Shift -Der **Lamb-Shift**, entdeckt von *Willis Lamb* und *Robert Retherford*, ist eine weitere Korrektur der Energieniveaus, die aus der Wechselwirkung der Elementarteilchen mit dem Vakuum resultiert, basierend auf der **Quantenelektrodynamik** und der **Quantenfeldtheorie**. Dargestellt durch Feynman-Diagramme, sind die drei größten Beiträge die Selbstenergie des Elektrons, die Vakuumpolarisation und die Vertexkorrektur. Diese Korrekturen zeigen, dass der Faktor $g_s$ zu $2 \left(1 + \frac{\alpha}{2 \pi} - 0.328 \frac{\alpha^2}{\pi^2} + \ldots\right) \neq 2$ korrigiert werden muss. Theoretische Berechnungen und experimentelle Messungen von $g_s - 2$ zeigen eine sehr gute Übereinstimmung, aber leichte Abweichungen weisen auf das komplexe Verhalten der Quantenelektrodynamik hin. Der **Lamb-Shift** hebt zudem die Entartung zwischen den Zuständen $2s_{\frac{1}{2}}$ und $2p_{\frac{1}{2}}$ auf und verändert die Bindungsenergie durch eine Absenkung des $\frac{1}{r}$-Potentials, was eine Änderung der Bindungsenergie um ca. $4.4 \times 10^{-6}$ eV zur Folge hat. +Der **Lamb-Shift**, entdeckt von *Willis Lamb* und *Robert Retherford*, ist eine weitere Korrektur der Energieniveaus, die aus der Wechselwirkung der Elementarteilchen mit dem Vakuum resultiert, basierend auf der **Quantenelektrodynamik** und der **Quantenfeldtheorie**. Dargestellt durch [[Feynman-Diagramme]], sind die drei größten Beiträge die Selbstenergie des Elektrons, die Vakuumpolarisation und die Vertexkorrektur. Diese Korrekturen zeigen, dass der Faktor $g_s$ zu $2 \left(1 + \frac{\alpha}{2 \pi} - 0.328 \frac{\alpha^2}{\pi^2} + \ldots\right) \neq 2$ korrigiert werden muss. Theoretische Berechnungen und experimentelle Messungen von $g_s - 2$ zeigen eine sehr gute Übereinstimmung, aber leichte Abweichungen weisen auf das komplexe Verhalten der Quantenelektrodynamik hin. Der **Lamb-Shift** hebt zudem die Entartung zwischen den Zuständen $2s_{\frac{1}{2}}$ und $2p_{\frac{1}{2}}$ auf und verändert die Bindungsenergie durch eine Absenkung des $\frac{1}{r}$-Potentials, was eine Änderung der Bindungsenergie um ca. $4.4 \times 10^{-6}$ eV zur Folge hat. ![[Ex4_0623_Vertex_correction.svg.png]] ![[Ex4_0623_Vacuum_polarization.svg.png]] ![[Ex4_0623_SelfE.svg.png]] diff --git a/content/fig/Feynman-Diagramme-Zusammenfassung.pdf b/content/fig/Feynman-Diagramme-Zusammenfassung.pdf new file mode 100644 index 0000000000000000000000000000000000000000..eb3335cc5d0124f50703f9219e19f50b526cf296 GIT binary patch literal 1093998 zcmV)cK&ZbZP((&8F)lL-CB)_ObY*fNFGg%( zbY(#BW~P=bh)k$|NK9mAOHDZjPC#a z%RfKqCejcTmNvGkKefX@d8-pCw%kqI~QMoYd7EJn~&eQ_yTOaq(aH<^X=mH@Dxo_~8Qla5uN#b@2iGRNvfw z4c^e*T@Ezaanm z@Dp#;_kU;TF9;m{grlFIe`o10$dLW;4JZ4;(aY~l{d_?#s(n{Do?m`v>o3T+$$!M- z`Q>-U{(^jap(7yAufHqkFUU_85<@({{;s0GAU|8^@%i<4C4E7DENgEUXa6Z{7v!fq 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